We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of co5nal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic (HA) is strongly comple...

Artikulu honetan, lehen pertsonako “ni” izenordainari buruz Kripkek dituenikuskerez ari naiz. Nire asmoa da erakustea Saul Kripkeren geroagoko ikuskera nola urruntzenden Naming and Necessityn esplikatu zituenetatik, eta John Perryren azalpenarekinalderatzea; gertuago dago Perryrena hasierako baieztapenetatik. biartikulu eztabaidatzen ditut, “Frege’s Theory of Sense Reference” “The First Person”...

A Kripke model K is a submodel of another Kripke modelM if K is ob tained by restricting the set of nodes ofM In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas This result is an analogue of the Lo s Tarski theorem for the Classical Predicate Calculus In appe...

A runtime verification technique has been developed for CSP via translation of CSP models to Kripke structures. With this technique, we can check that a system under test satisfies properties of traces and refusals of its CSP model. This complements analysis facilities available for CSP and for all languages with a CSP-based semantics: Safety-Critical Java, Simulink, SysML, and so on. Soundness...

BAN logic is a propositional logic of knowledge for the verification of cryptographic protocols. While BAN logic has been successful from a practical point of view, the semantics of the epistemic (knowledge) modality is unclear. Several Kripke semantics have been proposed, but they do not attempt at anything beyond a soundness result. Completeness is prevented by the so called logical omniscien...

IPV is IPV (which is essentially IS 2 ) with polynomial-induction on Σ 1 -formulas disjoined with arbitrary formulas in which the induction variable does not occur. This paper proves that IPV is sound and complete with respect to Kripke structures in which every world is a model of CPV (essentially S 2 ). Thus IPV is sound with respect to such structures. In this setting, this is a strengthenin...

We show that recent Model-driven Engineering that uses sequential finite state models in combination with a common sense logic is subject to efficient model checking. To achieve this, we first provide a formal semantics of the models. Using this semantics and methods for modeling sequential programs we obtain small Kripke structures. When considering the logics, we need to extend this to handle...

This paper presents some testing approaches based on model checking and using different testing criteria. First, test sets are built from different Kripke structure representations. Second, various rule coverage criteria for transitional, non-deterministic, cell-like P systems, are considered in order to generate adequate test sets. Rule based coverage criteria (simple rule coverage, context de...

In the first section of this paper we show that iΠ1 ≡ W¬¬lΠ1. In the second section of the paper, we show that for equivalence of forcing and satisfaction of Πm-formulas in a linear Kripke model deciding ∆0-formulas, it is necessary and sufficient that the model be Σm-elementary. This implies that if a linear Kripke model forces PEMprenex, then it forces PEM . We also show that, for each n > 1,...

Dynamic programs, or fixpoint iteration schemes, are useful for solving many problems on state spaces, including model checking on Kripke structures (“verification”), computing shortest paths on weighted graphs (“optimization”), computing the value of games played on game graphs (“control”). For Kripke structures, a rich fixpoint theory is available in the form of the μ-calculus. Yet few connec...